Collocation methods and error analyses for the semiconductor problem (Q2721798)
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scientific article; zbMATH DE number 1616536
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Collocation methods and error analyses for the semiconductor problem |
scientific article; zbMATH DE number 1616536 |
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27 March 2002
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semiconductor model
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electron and hole equations
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collocation method
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optimal error estimates
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energy estimates
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Dirichlet initial boundary value problem
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Collocation methods and error analyses for the semiconductor problem (English)
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The author uses collocation methods to study the numerical approximation of the Dirichlet initial boundary value problem for a semiconductor model in \(\mathbb{R}^n\) consisting of the electron and hole equations [cf. \textit{R. E. Bank}, \textit{W. M. Fichtner, D. J. Rose}, et al., IEEE Computer Aided Design 6, 436-451 (1985)] for the physical background of the model]. Assuming that the solutions are sufficiently smooth and that \(\Delta t=o(h^{n/2})\), and applying energy estimates and the discrete Gronwall's inequality, the author gives the optimal error estimate in \(L^2\)-norm.
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